Subgroups — #10624709⋊C₂ #13090966

Order 1458.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624709	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃⋊(D₂₇⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	#92294	—	3	1	no	maximal
4	AGL(1,ℤ/27)	—	3	3	no	maximal
5	C₃×C₂₇⋊C₃	—	2	1	no	—
6	C₃×C₂₇⋊C₃	C₂×C₃	1	1	yes	characteristic
7	#6887	D₃	1	1	yes	characteristic
8	#6875	—	2	3	no	—
9	#6875	D₃	1	3	yes	complemented
10	C₃×C₃⋊D₉	—	3	1	no	—
11	C₃⋊D₂₇	C₉	1	1	yes	characteristic, complemented
12	D₂₇⋊C₃	—	3	3	no	—
13	D₉⋊C₉	—	9	1	no	—
14	D₉⋊C₉	—	9	1	no	—
15	(C₃⋊D₃)⋊C₉	—	9	1	no	—
16	C₉×D₉	—	9	1	no	—
17	C₃²×C₉	C₃×D₃	1	1	yes	characteristic
18	C₂₇⋊C₃	—	2	3	no	—
19	C₂₇⋊C₃	—	2	3	no	—
20	C₂₇⋊C₃	—	6	1	no	—
21	C₂₇⋊C₃	—	6	1	no	—
22	C₂₇⋊C₃	C₃×D₃	1	3	yes	—
23	C₃×C₂₇	—	2	1	no	—
24	C₃×C₂₇	—	6	1	no	—
25	C₃×C₂₇	C₂×C₉	1	1	yes	characteristic, complemented
26	C₉⋊C₉	—	2	1	no	—
27	C₉⋊C₉	—	3	1	no	—
28	C₉⋊C₉	C₃⋊D₃	1	1	yes	characteristic
29	C₃²⋊C₉	—	3	1	no	—
30	C₉²	—	3	1	no	—
31	C₃×C₃⋊D₃	—	9	1	no	—
32	C₃⋊D₉	—	3	1	no	—
33	D₃×C₉	—	27	1	no	—
34	C₃×D₉	—	9	1	no	—
35	C₃×D₉	—	9	1	no	—
36	C₃×D₉	—	9	1	no	—
37	D₂₇	—	3	3	no	—
38	C₃³	AGL(1,ℤ/9)	1	1	yes	characteristic
39	C₃×C₉	—	2	1	no	—
40	C₃×C₉	—	2	1	no	—
41	C₃×C₉	—	2	1	no	—
42	C₃×C₉	—	2	1	no	—
43	C₃×C₉	—	3	1	no	—
44	C₃×C₉	—	6	1	no	—
45	C₃×C₉	D₃×C₉	1	1	yes	characteristic
46	C₃×C₉	AGL(1,ℤ/9)	1	1	yes	characteristic
47	C₃×C₉	AGL(1,ℤ/9)	1	1	yes	characteristic
48	C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
49	C₂₇	—	2	3	no	—
50	C₂₇	—	6	3	no	—
51	C₂₇	D₃×C₉	1	3	yes	—
52	C₃⋊D₃	—	9	1	no	—
53	C₃×D₃	—	27	1	no	—
54	C₃×D₃	—	81	1	no	—
55	C₂×C₉	—	81	1	no	—
56	D₉	—	9	1	no	—
57	D₉	—	9	1	no	—
58	D₉	—	9	1	no	—
59	C₃²	—	2	1	no	—
60	C₃²	—	9	1	no	—
61	C₃²	D₉⋊C₉	1	1	yes	characteristic
62	C₃²	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
63	C₉	—	2	1	no	—
64	C₉	—	2	1	no	—
65	C₉	—	2	1	no	—
66	C₉	—	9	1	no	—
67	C₉	—	18	1	no	—
68	C₉	D₉⋊C₉	1	1	yes	characteristic
69	C₉	D₉⋊C₉	1	1	yes	characteristic
70	C₉	C₉×C₃⋊D₃	1	1	yes	characteristic
71	C₂×C₃	—	81	1	no	—
72	D₃	—	27	1	no	—
73	D₃	—	81	1	no	—
74	C₃	—	3	1	no	—
75	C₃	—	3	1	no	—
76	C₃	—	6	1	no	—
77	C₃	C₃⋊(D₉⋊C₉)	1	1	yes	characteristic
78	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₃×C₂₇	C₂×C₉
Frattini	C₃×C₉	C₃×C₃⋊D₃
Fitting	#10624709	C₂
socle	C₃	C₃⋊(D₉⋊C₉)
prime radical	C₃⋊(D₂₇⋊C₃)	C₃
cosocle	C₃×C₂₇⋊C₃	C₂×C₃
LCS	G ▷ C₃×C₂₇
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #10624709	C₂	semidirect
9. #6875	D₃	semidirect
11. C₃⋊D₂₇	C₉	semidirect
25. C₃×C₂₇	C₂×C₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10624709	2
C₃⋊(D₂₇⋊C₃)	3
#92294	3
AGL(1,ℤ/27)	3

Subgroups — #10624709⋊C2 #13090966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10624709⋊C₂ #13090966